Translation and rotation of a spherical particle in a turbulent boundary layer

Abstract

Three-dimensional particle tracking experiments were conducted in a turbulent boundary layer with friction Reynolds number $Re_τ$ of 700 and 1300. Two finite size spheres with specific gravities of 1.003 (P1) and 1.050 (P2) and diameters of 60 and 120 wall units were released individually from rest on a smooth wall. The spheres were marked with dots all over the surface to monitor their translation and rotation via high-speed stereoscopic imaging. The spheres accelerated strongly after release over streamwise distances of one boundary layer thickness before approaching an approximate terminal velocity. Initially, sphere P1, which had Reynolds numbers $Re_p$ of 800 and 1900, always lifts off from the wall. Similar behavior was observed occasionally for sphere P2 with initial $Re_p$ of 1900. The spheres that lifted off reached an initial peak in height before descending towards the wall. The sphere trajectories exhibited multiple behaviors including saltation, resuspension and sliding motion with small random bouncing depending on both $Re_τ$ and specific gravity. The lighter sphere at $Re_τ=1300$, which remained suspended above the wall during most of its trajectory, propagated with the fastest streamwise velocity. By contrast, the denser sphere at $Re_τ=700$, which mostly slid along the wall, propagated with the slowest streamwise velocity. After the spheres approached an approximate terminal velocity, many experienced additional lift-off events that were hypothesized to be driven by hairpins or coherent flow structures. Spheres were observed to rotate about all three coordinate axes. While the mean shear may induce a rotation about the spanwise axis, near-wall coherent structures and the sphere's wake might drive the streamwise and wall-normal rotations. In all cases where the sphere propagates along the wall, sliding motion, rather than forward rolling motion, is dominant.